Growth model of the reared sea urchin Paracentrotus ... - SciViews

measures made at time t'i and I(u < v) returns 1 if true and 0 if false, as in
eq. 22. Parameters of the envelope model to fit, ξ2, are estimated by
minimizing the following objective function δ2:
δ 2 =
Part IV: A growth model with intraspecific competition
n
∑
i=
1
| D' −ξ
2( t' , ˆ τ )|
i i i
n
(37)
δ2 is indeed the mean absolute deviation between observed and predicted
sizes for all observations. A robust simplex minimization algorithm is used
to converge to the solution (Nelder & Mead, 1965; Nocedal & Wright,
1999).
Fitting of the envelope model (eq. 35) by minimizing δ2 is presented in
Fig. 33. This graph emphasizes how individual variation is now included
in the model itself. Gain is obvious by comparing it to Fig. 28A, where the
same dataset is summarized into less informative 2D-curves. Parameters of
the model are: k1 = 1.53 10 -3 , k2 = 3.65 10 -3 , s = 12.7, µ ∆ D = 57.0 and
∞
σ ∆ D = 4.28, deviance δ2 = 1.18.
∞
Fig. 34 is a diagnostic of this regression. Fig. 34A shows residuals (as
differences between observed and predicted values) using a contour plot.
There are only small patches of residuals above 2 mm or below –2 mm,
attesting a good fitting of the model. Residuals are not randomly
distributed. This is probably due to some autocorrelation in the dataset, to
some subtle environmental fluctuations in the rearing system (seasonal
variations…), or possibly to some lack of fit of the model.
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